def test_checkpointing(controlspace_t):
mesh = fd.UnitSquareMesh(5, 5)
if controlspace_t == fs.BsplineControlSpace:
bbox = [(-1, 2), (-1, 2)]
orders = [2, 2]
levels = [4, 4]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = fs.H1InnerProduct(Q)
q = fs.ControlVector(Q, inner)
p = fs.ControlVector(Q, inner)
from firedrake.petsc import PETSc
rand = PETSc.Random().create(mesh.comm)
rand.setInterval((1, 2))
q.vec_wo().setRandom(rand)
Q.store(q)
Q.load(p)
assert q.norm() > 0
assert abs(q.norm()-p.norm()) < 1e-14
p.axpy(-1, q)
assert p.norm() < 1e-14
def test_vectorkron():
""" Collection of tests."""
mesh = fd.UnitSquareMesh(1, 1)
bbox = [(0, 1), (0, 1)]
orders = [2, 2]
levels = [2, 2]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
# test
A = sp.sparse.csr_matrix(np.array([[0, 5, 7, 0, 9]]))
B = sp.sparse.csr_matrix(np.array([[1, 2, 0]]))
mytest_vectorkron(Q, A, B)
# test
A = sp.sparse.csr_matrix(np.array([[0, 2, 0, 5, 6]]))
B = sp.sparse.csr_matrix(np.array([[0, 2, 0, 5, 6]]))
mytest_vectorkron(Q, A, B)
# test
A = sp.sparse.csr_matrix(np.array([[]]))
B = sp.sparse.csr_matrix(np.array([[0, 2, 0, 5, 6]]))
mytest_vectorkron(Q, A, B)
# test
A = sp.sparse.csr_matrix(np.array([[1, 1.1, 10, 0, 2, 0, 5, 6]]))
B = sp.sparse.csr_matrix(np.array([[0, 2, 0, -3, 6]]))
mytest_vectorkron(Q, A, B)
# test
A = sp.sparse.csr_matrix(np.array([[0, 2, 0, 5, 6]]))
B = sp.sparse.csr_matrix(np.array([[]]))
mytest_vectorkron(Q, A, B)
# test
A = sp.sparse.csr_matrix(np.array([[0, 5, 6]]))
B = sp.sparse.csr_matrix(np.array([[1e3, 0, 2, 0, 5, 6]]))
mytest_vectorkron(Q, A, B)
def test_levelset(dim, inner_t, controlspace_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for fsz.LevelsetFunctional."""
clscale = 0.1 if dim == 2 else 0.2
# make the mesh a bit coarser if we are using a multigrid control space as
# we are refining anyway
if controlspace_t == fs.FeMultiGridControlSpace:
clscale *= 4
if dim == 2:
mesh = fs.DiskMesh(clscale)
elif dim == 3:
mesh = fs.SphereMesh(clscale)
else:
raise NotImplementedError
if controlspace_t == fs.BsplineControlSpace:
if dim == 2:
bbox = [(-2, 2), (-2, 2)]
orders = [2, 2]
levels = [4, 4]
else:
bbox = [(-3, 3), (-3, 3), (-3, 3)]
orders = [2, 2, 2]
levels = [3, 3, 3]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = inner_t(Q)
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# levelset test case
if dim == 2:
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(1.3 * y, 2) - 1.
elif dim == 3:
(x, y, z) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(0.8 * y, 2) + pow(1.3 * z, 2) - 1.
else:
raise NotImplementedError
J = fsz.LevelsetFunctional(f, Q, cb=cb, scale=0.1)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
# these tolerances are not very stringent, but solutions are correct with
# tighter tolerances, the combination
# FeMultiGridControlSpace-ElasticityInnerProduct fails because the mesh
# self-intersects (one should probably be more careful with the opt params)
grad_tol = 1e-1
itlim = 15
itlimsub = 15
# Volume constraint
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q, scale=1)
initial_vol = vol.value(q, None)
econ = fs.EqualityConstraint([vol], target_value=[initial_vol])
emul = ROL.StdVector(1)
# ROL parameters
params_dict = {
'Step': {
'Type': 'Augmented Lagrangian',
'Augmented Lagrangian': {
'Subproblem Step Type': 'Line Search',
'Penalty Parameter Growth Factor': 1.05,
'Print Intermediate Optimization History': True,
'Subproblem Iteration Limit': itlimsub
},
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
},
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 50
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': itlim
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q, econ=econ, emul=emul)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
# and that the volume has not changed too much
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)
assert abs(vol.value(q, None) - initial_vol) < 1e-2
import firedrake as fd
import fireshape.zoo as fsz
import fireshape as fs
import ROL
mesh = fs.DiskMesh(0.1)
bbox = [(-1.01, 1.01), (-1.01, 1.01)]
orders = [3, 3]
levels = [4, 4]
Q = fs.BsplineControlSpace(mesh,
bbox,
orders,
levels,
boundary_regularities=[0, 0])
inner = fs.H1InnerProduct(Q)
q = fs.ControlVector(Q, inner)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
f = (pow(x, 2)) + pow(2 * y, 2) - 1
outdef = fd.File("deformation.pvd")
out = fd.File("domain.pvd")
V, I = Q.get_space_for_inner()
T = fd.Function(V)
def cb():
out.write(mesh_m.coordinates)
Q.visualize_control(q, T)
def test_levelset(dim, inner_t, controlspace_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for fsz.LevelsetFunctional."""
clscale = 0.1 if dim == 2 else 0.2
# make the mesh a bit coarser if we are using a multigrid control space as
# we are refining anyway
if controlspace_t == fs.FeMultiGridControlSpace:
clscale *= 2
if dim == 2:
mesh = fs.DiskMesh(clscale)
elif dim == 3:
mesh = fs.SphereMesh(clscale)
else:
raise NotImplementedError
if controlspace_t == fs.BsplineControlSpace:
if dim == 2:
bbox = [(-2, 2), (-2, 2)]
orders = [2, 2]
levels = [4, 4]
else:
bbox = [(-3, 3), (-3, 3), (-3, 3)]
orders = [2, 2, 2]
levels = [3, 3, 3]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = inner_t(Q)
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# levelset test case
if dim == 2:
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(1.3 * y, 2) - 1.
elif dim == 3:
(x, y, z) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(0.8 * y, 2) + pow(1.3 * z, 2) - 1.
else:
raise NotImplementedError
J = fsz.LevelsetFunctional(f, Q, cb=cb, scale=0.1)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
"""
move mesh a bit to check that we are not doing the
taylor test in T=id
"""
g = q.clone()
J.gradient(g, q, None)
q.plus(g)
J.update(q, None, 1)
""" Start taylor test """
J.gradient(g, q, None)
res = J.checkGradient(q, g, 5, 1)
errors = [l[-1] for l in res]
assert (errors[-1] < 0.11 * errors[-2])
q.scale(0)
""" End taylor test """
grad_tol = 1e-6 if dim == 2 else 1e-4
# ROL parameters
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 50
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': 150
}
}
# assemble and solve ROL optimization problem
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)